This paper considers the computation of sparse solutions of the linear complementarity problems LCP(q, M). Mathematically, the underlying model is NP-hard in general. Thus an lp(0 p < 1) regularized minimization mo...This paper considers the computation of sparse solutions of the linear complementarity problems LCP(q, M). Mathematically, the underlying model is NP-hard in general. Thus an lp(0 p < 1) regularized minimization model is proposed for relaxation. We establish the equivalent unconstrained minimization reformation of the NCP-function. Based on the generalized Fiser-Burmeister function, a sequential smoothing spectral gradient method is proposed to solve the equivalent problem. Numerical results are given to show the efficiency of the proposed method.展开更多
In order to investigate physically meaning localized nonlinear waves on the periodic background defined by Weierstrass elliptic℘-function for the(n+1)-dimensional generalized Kadomtsev–Petviashvili equation by Darbou...In order to investigate physically meaning localized nonlinear waves on the periodic background defined by Weierstrass elliptic℘-function for the(n+1)-dimensional generalized Kadomtsev–Petviashvili equation by Darboux transformation,the associated linear spectral problem with the Weierstrass function as the external potential is studied by utilizing the Laméfunction.The degenerate solutions of the nonlinear waves have also been obtained by approaching the limits of the half-periodsω_(1) andω_(2) of℘(x).At the same time,the evolution and nonlinear dynamics of various nonlinear waves under different parameter regimes are systematically discussed.The findings may open avenues for related experimental investigations and potential applications in various nonlinear science domains,such as nonlinear optics and oceanography.展开更多
In this paper, we consider a class of nonlinear second-order singular Neumann boundary value problem with parameters in the boundary conditions. By the fixed point index, spectral theory of the linear operators, and l...In this paper, we consider a class of nonlinear second-order singular Neumann boundary value problem with parameters in the boundary conditions. By the fixed point index, spectral theory of the linear operators, and lower and upper solutions method, we prove that there exists a constant λ* > 0 such that for λ ∈ (0, λ * ), NBVP has at least two positive solutions; for λ = λ* , NBVP has at least one positive solution; for λ > λ* , NBVP has no solution.展开更多
The authors prove that flat ground state solutions(i.e. minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semilinear autonomous elliptic equat...The authors prove that flat ground state solutions(i.e. minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semilinear autonomous elliptic equations with a strong absorption term given by a non-Lipschitz function are unstable for dimensions N = 1, 2 and they can be stable for N ≥ 3 for suitable values of the involved exponents.展开更多
文摘This paper considers the computation of sparse solutions of the linear complementarity problems LCP(q, M). Mathematically, the underlying model is NP-hard in general. Thus an lp(0 p < 1) regularized minimization model is proposed for relaxation. We establish the equivalent unconstrained minimization reformation of the NCP-function. Based on the generalized Fiser-Burmeister function, a sequential smoothing spectral gradient method is proposed to solve the equivalent problem. Numerical results are given to show the efficiency of the proposed method.
基金supported by the National Natural Science Foundation of China (Grant Nos. 12475007 and 12171433)。
文摘In order to investigate physically meaning localized nonlinear waves on the periodic background defined by Weierstrass elliptic℘-function for the(n+1)-dimensional generalized Kadomtsev–Petviashvili equation by Darboux transformation,the associated linear spectral problem with the Weierstrass function as the external potential is studied by utilizing the Laméfunction.The degenerate solutions of the nonlinear waves have also been obtained by approaching the limits of the half-periodsω_(1) andω_(2) of℘(x).At the same time,the evolution and nonlinear dynamics of various nonlinear waves under different parameter regimes are systematically discussed.The findings may open avenues for related experimental investigations and potential applications in various nonlinear science domains,such as nonlinear optics and oceanography.
基金Supported by NNSF of China (No.60665001)Educational Department of Jiangxi Province(No.GJJ08358, No.GJJ08359, No.JXJG07436)
文摘In this paper, we consider a class of nonlinear second-order singular Neumann boundary value problem with parameters in the boundary conditions. By the fixed point index, spectral theory of the linear operators, and lower and upper solutions method, we prove that there exists a constant λ* > 0 such that for λ ∈ (0, λ * ), NBVP has at least two positive solutions; for λ = λ* , NBVP has at least one positive solution; for λ > λ* , NBVP has no solution.
基金supported by the projects of the DGISPI(Spain)(Ref.MTM2011-26119,MTM2014-57113)the UCM Research Group MOMAT(Ref.910480)
文摘The authors prove that flat ground state solutions(i.e. minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semilinear autonomous elliptic equations with a strong absorption term given by a non-Lipschitz function are unstable for dimensions N = 1, 2 and they can be stable for N ≥ 3 for suitable values of the involved exponents.
